We can state an alternative condition, also from [1]},
that \(X_j\)  is sub-Weibull with tail parameter \(\theta \)  if
\( \exists c > 0 \text{ s.t. } \forall t \geqslant 1: \Vert X_j \Vert _t \leqslant c t^{\theta }. \) 
